More Analysis of Gene Expression Data

Brent D. Foy, Ph.D.

Wright State University

Overview

• Types of Data Sets

• Data Analysis– Clustering

• Hierarchical

• Self-Organizing Maps

• Principal Components Analysis

– Statistical Hypothesis Testing (ANOVA)

Types of Data – 1D, 2 Conditions

• Many genes• 2 conditions• A few replicates

per condition

Gene Condition 1 Condition 2

Rep 1

Rep 2

Rep 3

Rep 1

Rep 2

Rep 3

A 150 160 150 180 190 180

B 50 40 45 50 45 40

C 800 760 680 400 450 425

…

Types of Data – 1D, 2 Conditions (cont)

• Conditions can be control vs treated, different cell types, different time points, etc.

• Typical Question – Which genes’ expression levels change due to condition?– T-test, Mann-Whitney, Comparison Analysis

Types of Data – 1D, Multiple Conditions

• Many genes

• Multiple conditions

• A few replicates per condition

Types of Data – 1D, Multiple Conditions (cont)

Gene Condition 1 Condition 2 Condition 3 …

Rep 1

Rep 2

Rep 3

Rep 1

Rep 2

Rep 3

Rep 1

Rep 2

Rep 3

A 150 160 150 180 190 180 150 155 135

B 50 40 45 50 45 40 80 90 105

C 800 760 680 400 450 425 200 220 400

…

Types of Data – 1D, Multiple Conditions (cont)

• Again, conditions can be treatments or chemicals, cell types, time points, etc.

• Typical question – Which genes’ expression levels change due to one or more conditions?

– 1-way ANOVA, Kruskal-Wallis

Types of Data – 1D, Multiple Conditions (cont)

• Typical question – Which genes’ expression levels behave similarly for all the conditions?– Self-Organizing Maps, Hierarchical Clustering,

Principal Components Analysis

• Typical question – Which conditions show similar expression levels among genes? (Toxicogenomic Fingerprint)– Hierarchical Clustering, Principal Components

Analysis, (Self-Organizing Maps)

Types of Data – 2D, Multiple x Multiple Conditions

• Many genes

• 2 Factors, multiple conditions per factor– For example, Factor 1 could be dose of a

chemical, and Factor 2 could be time point after dosing

• Multiple replicates per condition

Types of Data – 2D, Multiple x Multiple Conditions (cont)

Gene Dose 1 Dose 2 …

Time 1 Time 2 Time 1 Time 2 …

Rep 1

Rep 2

Rep 1

Rep 2

Rep 1

Rep 2

Rep 1

Rep 2

A 150 160 150 180 190 180 150 155

B 50 40 45 50 45 40 80 90

C 800 760 680 400 450 425 200 220

…

Types of Data – 2D, Multiple x Multiple Conditions (cont)

• Typical Question – Which genes’ expression levels change due to time? Due to dose? Due to an interaction between the two?– 2-way ANOVA

• Or, eliminate one of the dimensions and ask the same questions as before – At time 1, which doses show similar expression levels among genes?

Typical Applications of Clustering Algorithms

0

2

4

6

0 2 4 6

Gene A

Gen

e B

chem1 chem6

chem2chem3

chem4 chem5

Many samples/cell lines/chemicals,Many genes

Number of axes can be very large here

Many samples/cell lines/chemicals,Principal components of genes

0

2

4

6

0 2 4 6

Principal component 1

Pri

nci

pal

com

pon

ent

2

chem1chem6

chem2chem3

chem4 chem5

Typical Applications of Clustering Algorithms

Many genes, multiple time points.(Different letters represent different genes.)

0

2

4

6

0 2 4 6

T1

T2 A F

BC

D E

Number of dimensions (time points) can be greater than 2

Many genes, multiple doses

0

2

4

6

8

0 2 4 6 8

Dose 1

Dos

e 2

A

F

B

C

D

E

Reasons to cluster genes of similar behavior together?

Hierarchical Clustering

• Focus on 1D, multiple conditions type of data

• Here, group cell types according to similar gene response

Hierarchical Clustering (cont)Construct pairwise groupings of data elements based on similarity. Definition of similarity is typically the separation of data elements in n-dimensional space.

Chem 2

Chem 3

Chem 1

Chem 6

Chem 4

Chem 5

Generation 3 2 1 0# clusters 6 3 2 1

0

2

4

6

0 2 4 6

Gene A

Gen

e B

chem1 chem6

chem2chem3

chem4 chem5

0

1

2

3

4

5

6

0 2 4 6

Expression at T1 = 1 h

Exp

ress

ion

at T

2 =

4 h

A F

BC

D

E

Hierarchical clustering - chooses pairwise groupings based on distances between pairs of points

Once the two closest points are found, the two are grouped together, and a new point is placed at the average location of the old 2 points.

Hierarchical clustering

Advantages• Computationally efficient

• Produces tree-like structure

Disadvantage• Clusters are not optimal. Once

branches split, it’s permanent. There is no way to reevaluate whether it was the best division based on whole data set.

Principal Component Analysis

- Each data point is a single condition- Each axis is a linear combination of hundreds or thousands of gene expression levels

Principal Component Analysis

• Reduces the dimensionality of the data set– Thousands of genes are combined in a few linear

combinations to make 2 or 3 Principal Components (PC). Going from thousands of axes, with each axis representing the expression level for a gene, to 2 or 3 axes.

• These few PCs may capture most of the variability of the original data set

• Hope is that the first few PCs extract or expose the cluster structure of the original data set– i.e. Another clustering algorithm still needed after PCA

Principal Component Analysis – A Simple Example

0

10

20

30

40

50

60

70

80

0 2 4 6 8 10

Gene A expression

Gen

e B

Exp

ress

ion

PC1

Self Organizing Maps

• Partition data into specified number of groupings.

• Iterative procedure, so seeks to produce optimal clusters.

• K-means clustering is a specific form of the self-organizing map

Self Organizing Maps - General Procedure

Consider n data points in d-dimensional space. In the hypothetical data set, there are 6 data points (gene expression levels) in 2-dimensional space (2 time points). Say you want k = 3 clusters.

1. Select k of your data points to each be the original center of a cluster

2. Place the next data point in the nearest cluster

3. Compute the new location of the cluster center

4. Repeat the previous 2 steps for each data point

5. After all data is placed in a cluster, use final cluster centers as starting point for another iteration beginning at step 2.

Self Organizing Maps – Simple Example

0

2

4

6

0 2 4 6

Time

G ene A G ene B G ene C

G ene D G ene E G ene F

0

1

2

3

4

5

6

0 2 4 6

Expression at T1 = 1 hE

xpre

ssio

n at

T2

= 4

h

A F

BC

D

E

0123456

0 2 4 6Expression at T1 = 1 h

Exp

ress

ion

at T

2 =

4 h

A F

BC

DE

Let Genes A, B, and C be initial cluster centers.

0123456

0 2 4 6Expression at T1 = 1 h

Exp

ress

ion

at T

2 =

4 h

A F

BC

DE

Clusters after 1st pass

0123456

0 2 4 6Expression at T1 = 1 h

Ex

pre

ssio

n a

t T

2 =

4 h

A F

BC

DE

Clusters after 2nd pass

Self Organizing Maps – Simple Example

0

12

34

5

0 2 4 6

Time

G ene A G ene F

0

2

4

6

0 2 4 6

Time

G ene D G ene E

0

2

4

6

0 2 4 6

Time

G ene B G ene C

Self Organizing Maps – Larger example

• X-axis is time after dose

• Y-axis is normalized gene expression level

• Group ~1000 genes into 24 categories

Self Organizing maps - details to consider

• Several methods exist for choosing initial data points for clusters.

• How to choose the initial number of clusters.

• Method of recalculating cluster center after adding a new data point can be varied. How much ‘weight’ is given to new data point.

• Routines for merging and dividing clusters and detecting outliers can be added at each iteration.

Self Organizing maps

Advantages• Able to come closer to ‘optimal’ clustering

through iterations.• Doesn’t force a tree-structure on data

Disadvantage• Larger number of options for clustering means

that details of process may be hidden.

Data Preprocessing

• Filter data– Remove genes with expression levels in the noise– Focus on a group of genes with a particular function

• Normalize data– Subtract a control condition– Scale so that a gene whose expression level changes

from 5000 to 10000 looks the same as a gene whose expression level changes from 500 to 1000. One possibility is to scale all genes to mean of 0 and standard deviation of 1.

Detecting Statistically Significant Changes

• Consider 1D, multiple conditions

• 1-way ANOVA

• Similar tests for 1D, 2 condition data:– Fold changes– Tests Steve described in previous talk (Mann-

Whitney, Comparison Analysis)

1D, Multiple Condition Data

Gene Dose 1 Dose 2 Dose 3 …

Rep 1

Rep 2

Rep 3

Rep 1

Rep 2

Rep 3

Rep 1

Rep 2

Rep 3

A 150 160 150 180 190 180 150 155 135

B 50 40 45 50 45 40 80 90 105

C 800 760 680 400 450 425 200 220 400

…

1-Way ANOVA

• Question being asked is whether the expression level for each gene (taken one at a time) changes significantly as a function of dose.

• More specifically, it compares the variability within replicates for a given dose to the variability caused by changing the dose.

• If gene chip contains 1000 genes, then do 1000 ANOVAs.

• Consider “repeated measures ANOVA” if multiple measurements done on same animal

ANOVA for Hepatocytes exposed to Hydrazine, time 0

Source SS df MS F P

Columns 5566 2 2783 3.21 0.1798

Error 2602 3 867

Total 8168 5

2-way ANOVA

• Apply to 2D, multiple x multiple condition data sets

• Consider 3 doses, 5 time points per dose, 2 replicates per condition

• Can reveal significant effect of time, significant effect of dose, or a significant interaction between the two

• A “2-way repeated measures ANOVA” also exists

2-way ANOVA for Hydrazine Data – Output for 1 gene

Source SS df MS F P

Time 28724 4 7181 9.20 7.3e-4

Dose 1143 2 572 0.73 0.498

Time*dose 22940 8 2868 3.67 0.016

Error 10930 14 781

Total 64409 28

2-Way ANOVA – p-value Summary for 10 Genes

2-Way ANOVA – Dose effect

Red, 0 mMGreen, 50 mMBlue, 75 mM

2-way ANOVA – Time x Dose effect

Software

• Free– Eisen’s software Cluster, Treeview

• Hierarchical clustering, SOM

• http://rana.lbl.gov/

– Genecluster• SOM

• http://www-genome.wi.mit.edu/cancer/software/software.html

Software (cont)

• Commercial, gene-specific– Genelinker Gold

• PCA, clustering, SOM, statistics• http://microarray.genelinker.com/products.html#GeneLinkerG

old

– GeneSpring• PCA, clustering, SOM, statistics• http://www.sigenetics.com/cgi/SiG.cgi/Products/GeneSpring/i

ndex.smf

– Rosetta• PCA, clustering, SOM, ANOVA• http://www.rosettabio.com/products/resolver/default.htm

– Several others

Software (cont)

• Tools, not gene specific– Matlab– SPSS– SAS

• A useful web site, briefly summarizes many software packages, up-to-date– http://ihome.cuhk.edu.hk/~b400559/arraysoft.ht

ml

Collaborators

AFRL

Dr. John Frazier

Dr. Charles Wang

Dr. Victor Chan

AFOSR

Dr. Walt Kozumbo

AFIT

Dr. Dennis Quinn

Rebecca Olson

Tom Hopkins

2Lt Matt Campbell

WSU

Dr. Nick Reo

Dr. Steve Berberich

Dr. Tatiana Karpinets

Questions?